Least Common Multiple of 66 and 69

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 66 and 69 the smallest integer that is 1518 that is divisible by both numbers.

Least Common Multiple (LCM) of 66 and 69 is 1518.

LCM(66,69) = 1518

LCM of 66 and 69

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 66 and 69

LCM of 66 and 69 is 1518

Least common multiple can be found by multiplying the highest exponent prime factors of 66 and 69. First we will calculate the prime factors of 66 and 69.

Prime Factorization of 66


2 66
3 33
11 11
1

Prime factors of 66 are 2, 3,11. Prime factorization of 66 in exponential form is:

66 = 21×31×111

Prime Factorization of 69


3 69
23 23
1

Prime factors of 69 are 3,23. Prime factorization of 69 in exponential form is:

69 = 31×231

Now multiplying the highest exponent prime factors to calculate the LCM of 66 and 69.

LCM(66,69) = 21×31×111×231
LCM(66,69) = 1518

Factors of 66

List of positive integer factors of 66 that divides 66 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1, 3, 23, 69

Least Common Multiple of 66 and 69 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 66 and 69, than apply into the LCM equation.

GCF(66,69) = 3
LCM(66,69) = ( 66 × 69) / 3
LCM(66,69) = 4554 / 3
LCM(66,69) = 1518

Properties of LCM 66 and 69

(i) The LCM of 69 and 66 is associative

LCM of 66 and 69 = LCM of 69 and 66

Related Least Common Multiples of 66

Related Least Common Multiples of 69

Frequently Asked Questions on LCM of 66 and 69

1. What is the LCM of 66 and 69?

Answer: LCM of 66 and 69 is 1518.

2. What are the Factors of 66?

Answer: Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66. There are 8 integers that are factors of 66. The greatest factor of 66 is 66.

3. What are the Factors of 69?

Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.

4. How to Find the LCM of 66 and 69?

Answer:

Least Common Multiple of 66 and 69 = 1518

Step 1: Find the prime factorization of 66

66 = 2 x 3 x 11

Step 2: Find the prime factorization of 69

69 = 3 x 23

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 1518 = 2 x 3 x 11 x 23

Step 4: Therefore, the least common multiple of 66 and 69 is 1518.